The evolution of plasmid-carried antibiotic resistance
© Svara and Rankin; licensee BioMed Central Ltd. 2011
Received: 25 October 2010
Accepted: 19 May 2011
Published: 19 May 2011
Antibiotic resistance represents a significant public health problem. When resistance genes are mobile, being carried on plasmids or phages, their spread can be greatly accelerated. Plasmids in particular have been implicated in the spread of antibiotic resistance genes. However, the selective pressures which favour plasmid-carried resistance genes have not been fully established. Here we address this issue with mathematical models of plasmid dynamics in response to different antibiotic treatment regimes.
We show that transmission of plasmids is a key factor influencing plasmid-borne antibiotic resistance, but the dosage and interval between treatments is also important. Our results also hold when plasmids carrying the resistance gene are in competition with other plasmids that do not carry the resistance gene. By altering the interval between antibiotic treatments, and the dosage of antibiotic, we show that different treatment regimes can select for either plasmid-carried, or chromosome-carried, resistance.
Our research addresses the effect of environmental variation on the evolution of plasmid-carried antibiotic resistance.
The emergence of antibiotic resistance in pathogenic bacteria, both in hospital and community-acquired infections, represents a significant public health problem [1–5]. Bacterial cells are capable of transferring genes horizontally. This DNA transfer can take place in three ways, through plasmids, phages, or uptake of naked DNA . Plasmids are extra-chromosomal pieces of DNA, which are capable of replicating independently of the genome, and are particularly important in the spread of antibiotic resistance genes. Plasmids have been directly implicated in the acquisition of resistance to many antibiotics [7–14]. This is particularly problematic since plasmids can cross many species and genus barriers, and the rate of plasmid transfer has even been shown to increase in more heterogeneous communities . Plasmids thus allow resistance to spread and persist in niches that are not necessarily subject to antibiotics .
Methods and Results
The density-dependent death rate is given by a. This per capita death rate a depends on the density of cells in the population. In a population of wild-type cells this is simply n F , since there are no other cell types. We assume an antibiotic-induced fitness cost Am. Antibiotics can have two actions on a cell: they can either kill the bacteria (bactericidal antibiotics such as penicillin) or they can prevent reproduction (bacteriostatic antibiotics, such as tetracycline). Our model is general and does not differentiate between the two and could thus apply to either. From equation (1), at equilibrium, dn F /dt = 0, there are two equilibrium points, n F * = 0 and n F * = (r-mA)/a. This implies that the antibiotic will drive the host population extinct if mA > r. Thus, the higher the concentration of antibiotic, the more likely it is that wild-type will be eradicated.
Parameters used in the model
Density of wild-type/plasmid-free cells ('F' in figures)
Density of cells with resistance on the chromosome ('C' in figures)
Density of cells infected with a resistance-carrying plasmid ('Plasmids' in figures)
Density of cells infected with a non-coding plasmid ('B' in figures)
Density of cells with resistance both on the chromosome and on a plasmid ('CP' in figures)
Density of cells infected with a non-coding plasmid, and with resistance on the chromosome ('CB' in figures)
Total density of cells
N = n F +n C +n P +n B +n CP +n CB
Concentration of antibiotic
Rate of decay of antibiotic
Treatment dosage of antibiotic
Interval between antibiotic treatments
Intrinsic per-capita growth rate of cells
Extrinsic density-dependent death rate of cells
Death rate of non-resistant cells, due to antibiotic
Cost of antibiotic resistance when gene carried on chromosome
Cost of antibiotic resistance when gene carried on plasmid
Cost of plasmid carriage
Rate of horizontal transfer of plasmids
Rate of segregation
This shows that lower costs (in terms of x, s and c P ), higher rates of transfer of the plasmid given by β(r-mA)/a, or greater impact of the antibiotic on wild-type cells (given by mA) will all favour the invasion of plasmid resistance.
This shows that plasmids cannot invade the population if there are no wild-type cells (i.e. n F = 0). As the antibiotic will kill wild-type cells, cells with resistance on the chromosome will be favoured over cells with resistance on a plasmid if the antibiotic has substantially reduced the density n F of wild-type cells. Plasmid-carried resistance will also be favoured over chromosome-carried resistance if the costs of expressing a resistance gene on the chromosome c C , is greater than the cost of expressing a resistance gene on a plasmid c P .
This shows that higher transfer rates β of the plasmid, as well as a greater effect of the antibiotic, or lower overall costs from carrying the plasmid (x +s + c p ) will all result plasmid-carried resistance have a greater over all rate of spread than wild-type cells. Interestingly, greater growth rates r will also favour plasmid-carried resistance to have a larger growth rate than wild-type cells.
Numerical analysis model
Model with non-coding plasmids
In the basic model, plasmids were favoured due to their ability to transfer infectiously. In the absence of antibiotics, non-resistant plasmids will outcompete resistance plasmids, because resistance plasmids additionally pay the cost of antibiotic resistance gene expression c P . As in the basic model, we assume that the antibiotic degrades at an exponential rate described by equation 6. We analyse the system described by equations 9-14 using the numerical method described in the previous section, but here we start at the point where both n F and n B have reached equilibria (i.e. the population already consists of wild-type cells and non-resistant plasmids coexisting), before introducing a small number of cells with resistance on the plasmid, or on the chromosome, respectively (i.e. nP = 0.01, nC = 0.01, nCP = 0, nCB = 0 at the start of the simulation).
We further explored our results for different parameter value combinations, such as the transmission rate (Additional Files 1 and 2), the segregation rate (Additional File 3), the respective cost of having resistance on a plasmid or a chromosome (Additional File 4) and the mortality cost m and the degradation rate l of the antibiotic (Additional File 5). All graphs can be found in the supplementary material. Our results generally held when changing these parameter values.
Plasmids are favoured when their rate of horizontal transfer outweighs the costs involved in plasmid carriage to a cell . However, in the presence of less costly plasmids, the benefit of transfer disappears . In our basic model in the absence of non-resistant plasmids, plasmids can persist as long as the rate of transfer is sufficient (Figure 3, Additional File 1). Our full model, incorporating non-resistant plasmids, shows that resistant plasmids outcompete non-resistant plasmids under higher dosages, and outcompete cells which resistance on the chromosome under longer intervals between treatments (Figures 5 and 6). This is due to horizontal gene transfer: wild-type cells are common when treatment is weak and their presence allows plasmids to invade. Resistance genes encoded by the host genome are favoured by treatment regimes that result in a continual presence of antibioitic. We can understand this intuitively by considering that the infectious maintenance of plasmids in a population consisting only of plasmid-carrying and wild-type cells requires the availability of plasmid-free cells. This is because carrying a plasmid and expressing resistance has a cost which has to be offset by the benefit of infecting susceptible cells. When susceptible cells are killed by antibiotics, plasmids suffer indirectly as they have fewer cells to infect. It is worth noting that our model assumes relatively efficient horizontal transfer, and thus our results may change if plasmids do not transmit themselves well. Our model would therefore predict that plasmids with lower transmission rates would not carry genes for antibiotic resistance. However the generality of our model of horizontal transfer of plasmids means that our findings will apply to other vehicles of gene transfer, such as phages.
We assumed that chromosomal- and plasmid-borne resistant types were phenotypically identical. This may not be the case  as changes in gene dosage can influence the resistance level [42–47]. We predict that higher gene dosage from multi-copy plasmids would enlarge the treatment space beneficial to plasmids, due to the additional resistance compared to chromosomally carried resistance genes. In the absence of antibiotics, hosts carrying multiple copies of resistance genes would be at a disadvantage due to the extra cost of producing more antibiotic resistance proteins. An important result of our study is to illustrate how the ecology of the bacteria, in this case the density of wild-type cells (mediated by the concentration of antibiotic), affects the conditions under which plasmid-borne resistance is favoured.
Our model makes qualitative predictions regarding the conditions under which antibiotic resistance genes will be selected to be carried on plasmids, as opposed to on the chromosome. Specifically, we were interested in asking whether the intensity and interval between treatments will select for resistance to be on a plasmid, or on a chromosome. However, we find that our results generally hold under a wide range of different parameter ranges (see supplementary material for details). There is a wide range of literature available with which such models could be parameterised, and it would be possible to design models to test when selection will result in resistance to be carried on plasmids. For example, it is possible to add more realism to model the pharmacodynamics of drugs and how they kill bacteria [e.g. [40, 48]], and there are some studies from which the costs of antibiotic resistance can be estimated [for example, see references in ]. Rates of horizontal gene transfer range widely and in the case of conjugation can range between 10-3 and 10-1 per donor in biofilms and more than 10-5 in water or soil [50–52]. As plasmids have been described as the Achilles' heal of drug resistant bacteria [53, 54], understanding the conditions under which antibiotic resistant genes are carried by plasmids could help to develop strategies to minimise the spread of resistance . Developing and parameterising more explicit models in combination with laboratory studies, in contrast to the simple qualitative models described here, will be essential to developing treatments than minimise the rates of transfer.
The use of multiple antibiotics and antibiotic cycling has been proposed as a way to prevent the evolution of antibiotic resistance [e.g. ]. A previous study showed that plasmids could play a role in the acquisition of multiple drug resistance by repeated gene transfer . Thus, plasmids may reduce the effect of antimicrobial cycling, as multiple resistance could be acquired more quickly. In the case of multidrug therapy, we would predict that the results of our model would hold, and longer intervals between treatment regimes would favour plasmid-carried resistance, which would in turn favour the evolution of multiple resistance.
Given the biological variability in the mechanisms of resistance, horizontal transfer and persistence, some of our assumptions may not hold in specific settings. Our work rests on costly antibiotic resistance and should thus apply particularly to mechanisms that need to be strongly expressed or that require a lot of cellular energy. When resistance proteins catalyse reactions that modify the antibiotic, such as in the case of β-lactamases, chloramphenicol acetyltransferase or aminoglycoside acetyltransferases, a higher expression level is expected to translate to a higher resistance level and the cell will have to pay high protein synthesis costs in order to be resistant. The same is true for efflux pumps, such as ABC -transporters or MF-type pumps . The cost of resistance plasmids, including the cost of maintenance and expression, could be significantly ameliorated in experimental evolution experiments [58–60]. Based on the above arguments and the fact that even small costs are significant over evolutionary timescales, we expect there to be a large number of environments in which our findings would hold despite this effect, but it illustrates that with respect to the clinical view on this fundamental problem, more detailed case-by-case analyses will be required.
To the best of our knowledge, our study represents the first model to explicitly examine the effect of treatment regimes plasmid-borne antibiotic resistance. We show that high transmission favours plasmid-carried resistance, in the absence of competing non-resistant plasmids. When other plasmids are present, low frequency treatments favour plasmid-carried resistance over chromosomal resistance, but a high intensity of antibiotic is needed for resistance plasmids to outcompete non-resistance plasmids. Targeting plasmid spread has been proposed to manage antibiotic resistance  and our results suggest that paying attention to the treatment regime is an essential requirement of any such strategy. The solution, as recommend by Paul Ehrlich almost a century ago, is to "hit hard and hit quickly" . Gaining a quantitative understanding of the dynamics of plasmids will allow us to understand harmful patterns of antibiotic use more effectively.
We thank Sam Brown, Jeffrey Lawrence, Sorcha Mc Ginty, Roland Regoes, jeff smith and three anonymous reviewers for helpful comments on the manuscript. We also thank Evandro Ferrada for help obtaining the genome data used in Figure 1, the Swiss National Science Foundation (grants 31003A-125457 and PZ00P3-121800) and the University of Zürich (both to DJR) for funding.
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